Yes you'd lose weight, but bear in mind you would crank your Metabolism up with running and increase Fat burning potential, but when you drank the shake, most or all of the additional fat burning potential, would be sacrificed when the body concentrated its efforts on processing the shake.

So don't hold store in this notion, that exercise allows you to burn more fat for hours afterwards, as it doesn't. Additional fat burning potential beyond what sedentry living can achieve, would start to decrease in part or possibly in full, within 20 minutes of consuming any kind of nutrition.

So should I go jogging after I eat dinner? And wait to drink the shake right after the run? The reason I drink the protein is because it really helps with the soreness the next day obviously because it's a workout shake. So drinking the shake right after is pointless because my body is working that off so it's back where it's started before the run right?